An enhanced chimp optimization algorithm for optimal degree reduction of Said–Ball curves

Abstract

Because of its good geometric characteristics, Said–Ball curve has become a useful tool for shape design and geometric representation in product manufacturing. In this paper, an enhanced chimp optimization algorithm (CHOA, for short) is used to solve the problem of approximate multi-degree reduction of Said–Ball curve. Firstly, two strategies are used to improve the optimization performance of original CHOA, and an enhanced version of CHOA named SOCSCHOA combined with selective opposition and cuckoo search is presented. Furthermore, according to the idea of multi-degree reduction of Said–Ball curve, the problem of multi-degree reduction of Said–Ball curve is transformed into an optimization problem, and the presented SOCSCHOA is applied to the solutions of the optimization model of the problem. Finally, the approximate multi-degree reductions of Said–Ball curve with and without endpoint preserving interpolation are realized, and the errors of the degree reduction are also given, which is compared with the availability of degree reduction of other intelligent algorithms. Numerical examples provided show that the proposed method not only achieves a good effect of degree reduction, but also is easy to implement with high accuracy.